4-1 結論
本次校內計畫完成了以下工作：
1. 利用現有堪用之硬體設備，架設完成一套簡易的 PC Cluster，包含一個伺服器 與六個計算節點(nodes)。軟體則選用 Linux 免費的作業系統，並安裝相關之 排程派送軟體與MPI 等相關函式庫。
2. 測試有限元素法四面體元素之一階形狀函數效能。
3. 發展有限元素法四面體元素之二階形狀函數。
4. 建立相關 Poisson-Boltzmann equation 在平行化系統上的應用。
4-2 建議
程式的效能與網路速度、電腦硬體(CPU、記憶體)息息相關，所以若能使用更好的 設備，則可以增加運算能力。此外，整個系統是由數部 PC 所組成，對於電力配置與 散熱的考量也要重新做一些規劃才行。
參考文獻
1. 精通 FORTRAN90 程式設計，碁峰出版社，彭國倫著，1997 年版
2. FORTRAN 語言 MPI 平行計算程式設計，國家高速電腦中心，鄭守成著，90 年版
3. http://www.nm.ncku.edu.tw/cname/computer/for/for5.html
4. J.-S. Wu, T.-C. Cheng, Y.-L. Shao and C.-H. Wu, " Development of a Micro-PIV System and Its Applications ", The 11th Symposium on Nano Device Technology (SNDT 2004).
5. 吳宗信, 邵雲龍, 黃柏誠, 鄭宗杰, "微混合器之製作與研究," 奈米通訊, Vol.12, I1, pp.21-27, 2005.
6. J.-S. Wu and Y.-L. Shao, "Comparison of the Micro-PIV Measurements with Lattice Boltzmann Method in Micro-Channel Flows," The 11th National CFD Conference, Tai-Tung, Taiwan, August, 2004. (One of the three Best Paper Awards out of 190 papers).
7. J.-S. Wu, Y.-L. Shao,C.-H. Wu and T.-C. Cheng, " Design, Manufacture and Performance Analysis for a MicroMixer ", The 11th Symposium on Nano Device Technology (SNDT 2004)
8. J.-S. Wu and Y.-L. Shao, "Simulation of Lid-Driven Cavity Flows by Rarallel Lattice Boltzmann Method Using Milti-Relaxation Time Scheme,"International Journal for Numerical Methods in Fluids, Vol.46, pp.921-937, 2004.
9. J.-S. Wu and Y.-L. Shao, "Simulation of Flow Past a Square Cylinder by Parallel Lattice Boltzmann Method Using Multi-Relaxation-Time Scheme," Journal of Mechanics, Vol.22, No.1, pp.35-42, 2006.
10. Y.-Y. Lian, K.-H. Hsu, Y.-L. Shao, Y.-M. Lee, Y.-W. Jeng and J.-S. Wu, ”Parallel Adaptive Mesh-Refining Scheme on Three-dimensional Unstructured Tetrahedral Mesh and Its Applications,” Computer Physics Communications, 2006 (Accepted).
11. Pavel Dyshlovenko, “Adaptive Mesh Enrichment for the Poisson-Boltzmann Equation,” Journal of Computation Physics, 172, pp.198-208, 2001.
12. J.-S. Wu, and C.-K. Tseng, "Analysis of Micro-scale Gas Flows With Pressure Boundaries Using The Direct Simulation Monte Carlo Method," Computers &
Fluids, Vol. 30, pp. 711-735, 2001.
13. Jeffrey D. McDonald, “A Computationally Efficient Particle Simulation Method Suited to Vector Computer Architectures.” PhD Thesis, Standford University, 1989.
14. D.M. Nicol and J.H. Saltz, "Dynamic Remapping of Parallel Computations with Varying Resources Demands," IEEE Transactions on Computing, Vol. 37, 1998, pp.
1073-1087.
15. Das, P.K. and Bhattacharjee, S., “Finite Element Estimation of Electrostatic Double
Layer Interaction between Colloidal Particles inside a Rough Cylindrical Capillary:
Effect of Charging Behavior,” Colloids and Surface A, Vol.256, pp.91-103, 2005.
16. Dyshlovenko, Pavel, “Adaptive numerical method for Poisson-Boltzmann equation and its application,” Computer Physics Communications, Vol.147, pp.335-338, 2002.
17. Gilson, M. K., Davis, M. E., Luty, B. A. and McCammon, J. A., "Computation of electrostatic forces on solvated molecules using the Poisson-Boltzmann equation,"
Journal of Physical Chemistry, Vol.97, pp.3591–3600, 1993.
18. Holst, M., Baker, N. and Wang ,F., “Adaptive multilevel finite element solution of the Poisson-Boltzmann equation I. Algorithms and examples, Journal of
Computational Chemistry, Vol.21, pp.1319-1342, 2000.
附錄一 文字編輯器 pico
pico 雖然不是 Linux 所內定的文字編輯器，但是因為操作方式還蠻簡單的，非常適 合新手使用。進入文字編輯器的方式，為輸入pico 檔案名稱，例如 pico test.f 接下來的操作方式，如下表所示，比較重要的功能加上網底，請熟記。
^G 求助
^F 移動游標往右一個字元
^B 移動游標往左一個字元
^P 移動游標往上一列
^N 移動游標往下一列
^A 移動游標往列首
^E 移動游標往列尾
^V 顯示下一頁的內容
^Y 顯示上一頁的內容
^W 尋找字串 (不管大小寫)
^L 刷新螢幕的顯示
^D 刪除游標上的字元
^^ (^6) 開始標記資料
^K 剪下整列的資料(也可以當作刪除整列的資料)
^U 緩衝區內容貼上游標之位置
^I 插入TAB(定位鍵)
^J 對齊段落
^C 報告游標目前之位置
^R 將一個檔案的內容插入游標所在的位置
^O 儲存現在檔案的內容
^X 儲存現在檔案內容並離開編輯器
附錄二 二階四面體 Shape function 函數
The volume integrals can be easily evaluated from the relation
d V
We can use the equation to develop the volume integral, then
⎪⎪
))
)]
附錄三 一階四面體 Shape function 函數
中 其
4 4 4
3 3 3
2 2 2
1
z y x
z y x
z y x
a
=
,4 4
3 3
2 2
1
1 1 1
z y
z y
z y
b
= −
,4 4
3 3
2 2
1
1 1 1
z x
z x
z x
c
= −
and1 1 1
4 4
3 3
2 2
1
y x
y x
y x d
= −
四面體座標定義